A371786 a(n) = Sum_{k=0..floor(n/2)} (-1)^k * binomial(4*n-k,n-2*k).

1, 4, 27, 209, 1716, 14553, 125971, 1105885, 9809019, 87691592, 788832045, 7131655908, 64743390321, 589808771881, 5389066722654, 49365637128655, 453212161425716, 4168951499299185, 38415242186255419, 354527945536409116, 3276414018301664025

Offset

0,2

Links

Table of n, a(n) for n=0..20.

Formula

a(n) = [x^n] 1/((1-x+x^2) * (1-x)^(3*n)).

From Seiichi Manyama, Nov 10 2025: (Start)

G.f.: g/((1-4*x*g^3) * (1+x*g^5)) where g = 1+x*g^4 is the g.f. of A002293.

a(n) = Sum_{k=0..n} binomial(2*n+2*k-1,k).

a(n) = Sum_{k=0..n} (-1)^k * binomial(4*n+k+1,n-k). (End)

Prog

(PARI) a(n) = sum(k=0, n\2, (-1)^k*binomial(4*n-k, n-2*k));

Crossrefs

Cf. A024718, A371785, A371787.

Cf. A002293, A371743.

Sequence in context: A026005 A386959 A059391 * A390687 A190738 A361717

Adjacent sequences: A371783 A371784 A371785 * A371787 A371788 A371789

Keyword

nonn

Author

Seiichi Manyama, Apr 06 2024

Status

approved